Exercise 9.  Here we establish the validity of Inequality (4-17) in the proof of Theorem 4.17.  

9 (a).  Show that

where s and t are arbitrary complex numbers,  .  

Solution 9 (a).

See text and/or instructor's solution manual.

Solution  All that is necessary here is to carry out the following simplification:

                      
                    
Then divide by    and get  

                    

The conclusion follows from the triangle inequality

                    

This solution is complements of the authors.

(c) 2008 John H. Mathews, Russell W. Howell